Here the word "expectation" and the phrase "hope" mean basically the same thing. Paul uses them together to emphasize how strong his expectation is. Alternate translation: "I eagerly and confidently hope" (See: [[rc://en/ta/man/translate/figs-doublet]])
The phrase "in my body" is a metonym for what happens to Paul's body. This includes what he does if he lives and what others may do to him, even if they kill him. This can be stated in active form. Possible meanings are 1) "I will honor Christ no matter what happens to my body" or 2) "people will praise Christ no matter what I do or what others do to me" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-activepassive]])